Introduction to Deep Learning
McCulloch & Pitts show that neurons can be combined to construct a Turing machine (using ANDs, ORs, & NOTs).
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1943: McCulloch and Pitts – Turing Machines
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1958: Rosenblatt – Exercise (OR)
\[
f(x) =
\begin{cases}
1 & \sum_{i=1}^m w_i x_i + b > 0\\
0 & \text{otherwise}
\end{cases}
\]
tt_or <- tibble(
a = c(0, 0, 1, 1),
b = c(0, 1, 0, 1),
r = c(0, 1, 1, 1)
) %>% print()
1958: Rosenblatt – Exercise (AND)
\[
f(x) =
\begin{cases}
1 & \sum_{i=1}^m w_i x_i + b > 0\\
0 & \text{otherwise}
\end{cases}
\]
library(tidyverse)
tt_and <- tibble(
a = c(0, 0, 1, 1),
b = c(0, 1, 0, 1),
r = c(0, 0, 0, 1)
) %>% print()
1969: Minsky and Papert – Book (1/3)
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1969: Minsky and Papert – Book (2/3)
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1969: Minsky and Papert – Exercise (XOR)
\[
f(x) =
\begin{cases}
1 & \sum_{i=1}^m w_i x_i + b > 0\\
0 & \text{otherwise}
\end{cases}
\]
tt_xor <- tibble(
a = c(0, 0, 1, 1),
b = c(0, 1, 0, 1),
r = c(0, 1, 1, 0)
) %>% print()
1969: Minsky and Papert – Solution (XOR)
tt_xor <- tibble(
a = c(0, 0, 1, 1),
b = c(0, 1, 0, 1),
r = c(0, 1, 1, 0)
) %>% print()
w <- matrix(c( 0.5, 0.5, 0,
-0.5, -0.5, 1,
0.5, 0.5, -0.5), ncol = 3, byrow = T)
yh1 <- ifelse(x %*% w[1,] > 0, 1, 0)
yh2 <- ifelse(x %*% w[2,] > 0, 1, 0)
x3 <- matrix(c(yh1, yh2, c(1,1,1,1)), ncol = 3)
ifelse(x3 %*% w[3,] > 0, 1, 0)